Dog for breaking up demo, say (7)
I believe the answer is:
samoyed
'dog' is the definition.
(Samoyed is an example)
'breaking up demo say' is the wordplay.
'breaking up' indicates anagramming the letters.
'demo'+'say'='demosay'
'demosay' anagrammed gives 'SAMOYED'.
'for' acts as a link.
(Other definitions for samoyed that I've seen before include "Dog similar to chow" , "Dog - someday (anag)" , "Sled dog" , "Some day (anag) - dog (from Siberia?)" , "[HOUND] ?" .)